Symmetry and self-affinity or scale invariance are related concepts. We explore the fractal properties of fluctuations in dynamical systems, using some of the available tools in the context of time series analysis. We carry out a power spectrum study in the Fourier domain, the method of detrended fluctuation analysis and the investigation of autocorrelation function behavior. Our study focuses ...

We present a detailed investigation, qualitative and quantitative, on how the atmospheric turbulence with a non-Kolmogorov power spectrum affects the major statistics of stochastic electromagnetic beams, such as the spectral composition and the states of coherence and polarization. We suggest a detailed survey on how these properties evolve on propagation of beams generated by electromagnetic G...

This paper presents a new nonlinear method to analyze ventricular arrhythmia(VA) and sinus rhythms(SR). The problem is introduced from the discussion of Fractal Random Walk characteristics of ECG signal. Further, the fractal analysis is used to distinguish ventricular flutter(VFL), ventricular fibrillation(VF), ventricular tachycardia(VT)) and sinus rhythms(SR) from the raw electrocardiogram(EC...

The power spectrum S of linear transects of the earth's topography is often observed to be a power-law function of wave number k with exponent close to ?2: S(k) / k ?2. In addition, river networks are fractal trees that satisfy several power-law relationships between their morphologic components. A model equation for the evolution of the earth's topography by erosional processes which produces ...

Fractal analysis is a method of characterizing complex shapes such as the trabecular structure of bone. Numerous algorithms for estimating fractal dimension have been described, but the Fourier power spectrum method is particularly applicable to self-affine fractals, and facilitates corrections for the effects of noise and blurring in an image. We found that it provided accurate estimates of fr...

The D fractional Brownian motion fBm model is useful in describing natural scenes and textures Most fractal estimation algorithms for D isotropic fBm images are simple extensions of the D fBm estimation method This method does not perform well when the image size is small say We propose a new algorithm that estimates the fractal parameter from the decay of the variance of the wavelet coe cients...

The α predominant electroencephalographic (EEG) recording of the human brain during eyes-closed and-open is studied using the zero-crossing time statistics. We found evidence of fractal characteristics which is otherwise ambiguous from the power spectrum or detrend fluctuation analysis. Our results indicate a reverse relationship between the degree of fractal fluctuation and the α rhythm intens...

masjed soleyman dam site is located in the zagros mountain of western iran, which is one of the most seismically active zones of the alpe-himalayan belt. after impounding of dam, the seismicity of area increased considerably, showing the impact of reservoir (177 m height, 261 million m3) in changing the rate of seismicity in the area. we have analyzed the seismicity of area in terms of the spat...

We study the properties of spectrum and eigenstates of the Google matrix of a directed network formed by the procedure calls in the Linux Kernel. Our results obtained for various versions of the Linux Kernel show that the spectrum is characterized by the fractal Weyl law established recently for systems of quantum chaotic scattering and the Perron-Frobenius operators of dynamical maps. The frac...